{
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  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Problem definition\n",
    "\n",
    "Create some data, in this case a parabola plus white noise:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "scrolled": false
   },
   "outputs": [
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     },
     "execution_count": 1,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "using Plots\n",
    "gr(size=(1000,500))\n",
    "\n",
    "srand(2017)\n",
    "\n",
    "N = 100\n",
    "x = linspace(0,1, N)\n",
    "y = x.^2 .+ [i/1000*randn() for i=1:N]\n",
    "\n",
    "scatter(x, y, label=\"data\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Define the problem:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1D EstimationProblem\n",
       "  data:      100×2 GeoDataFrame (features)\n",
       "  domain:    100 RegularGrid{Float64,1}\n",
       "  variables: response (Float64)"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "using GeoStats\n",
    "\n",
    "data = DataFrames.DataFrame(features=x, response=y)\n",
    "geodata = GeoDataFrame(data, [:features])\n",
    "domain = bounding_grid(geodata, [N])\n",
    "\n",
    "problem = EstimationProblem(geodata, domain, :response)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Solver options\n",
    "\n",
    "The user can specify the number of neighbors (default to all data locations), a kernel (or weight) function (default to `ExponentialKernel`), and a metric from the [Distances.jl](https://github.com/JuliaStats/Distances.jl) package (default to Euclidean)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1D EstimationSolution\n",
       "  domain: 100 RegularGrid{Float64,1}\n",
       "  variables: response"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "using LocallyWeightedRegression\n",
    "\n",
    "solver = LocalWeightRegress(\n",
    "    :response => @NT(kernel=ExponentialKernel(10.))\n",
    ")\n",
    "\n",
    "solution = solve(problem, solver)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
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     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "results = digest(solution)\n",
    "\n",
    "yhat = results[:response][:mean]\n",
    "yvar = results[:response][:variance]\n",
    "\n",
    "scatter(x, y, label=\"data\")\n",
    "plot!(x, yhat, ribbon=yvar, fillalpha=.5, label=\"LWR\")"
   ]
  }
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